In the new “Fargo” TV series, Billy Bob Thornton’s character cuts like a cold wind through the folksy Minnesota accents and talk of meatloaf and Jell-O salads. He plays Lorne Malvo, a fixer/hit man who ends up in the town of Bemidji, where he meets the hapless Lester Nygaard (Martin Freeman). It’s not his job to do so, but Malvo can’t resist messing with Lester’s life in a deadly fashion.

Thornton was the first actor approached for “Fargo,” a 10-episode “limited series” which premiered Tuesday night on FX. Not only did he check the box of serious-film-actor-migrating-to-TV, he also brought a connection to Joel and Ethan Coen. (The brothers wrote, produced and directed the original “Fargo” film, and though they are executive producers of the TV series, they’re not closely involved with it.) Thornton starred in the Coens’ “Intolerable Cruelty” and “The Man Who Wasn’t There,” along with “Bad Santa,” which they executive produced.

In a recent interview, Thornton led off with a tangent about golf and public apologies, but then got down to discussing the reptilian nature of his “Fargo” character, and the chances of a sequel to “Sling Blade,” the film that launched his career in 1996, the same year that “Fargo” was released.

[Series writer/producer] Noah Hawley says the show started in his mind with the image of your character sitting next to a stranger, Martin Freeman’s character, in a hospital waiting room. These people couldn’t be more different.

Sometimes you have to think about your backstory and how you’re going to interact with the other actor and the chemistry. In this case, it’s two guys who don’t know each other and they’re night and day, so you just sit down and do it. I’m not worried about what he’s doing. I just do what I do.

What did you see in this script that made you to jump on this project? Because there’s a long list of reasons why this show might not have worked.

Let’s say “Fargo” [the movie] came out in 1986 and this was 1996, then I would have thought of it in a different way. Because these days, to get anybody to say anything decent about anybody is like pulling teeth. See, I don’t think Tiger Woods owes the public an apology. Name a golfer who doesn’t like hookers. Seriously. Tiger Woods owes an apology to his wife. That’s it. He doesn’t owe the public an apology. We live in a time where the public is the star, the judge, the court, everything. The audience has become the star. Because of that, you’re screwed already. So all this has actually had the opposite effect on me than you’d think it would. I don’t worry about anything. If I said something outrageous to you today and you put it in the Wall Street Journal, the next day my career could be in jeopardy. Now if I give an apology, the public says, “He’s only apologizing for his career.” If I don’t apologize, I’m an a–hole. In other words, you can’t win. So if you say, “Did you have any hesitation because ‘Fargo’ is a classic movie and the TV show is going to be compared?” No. None whatsoever. It’s no more dangerous doing this than something that’s just been invented.

But what was in the script that made you commit to a 10-hour TV show?

What spoke to me in the script was that Noah had captured the spirit and the vibe of the Coen brothers without imitating them. The only concern I had was whether the Coen brothers were on board, because they’re my friends. The fact that they were executive producers and had given their blessing, that was important. I called Bill Clinton when I did “Primary Colors” (1998), because I’ve known him since I was 18. I told him I was about to play a [James] Carville-like character and asked, “Would you be pissed off I did this?” He goes, “Are you kidding me? That’s a great part.”

Did you have a conversation with the Coens about the show?

They’re funny. They’re nonplussed about things. I talked to Ethan about a month ago. He said, “What are you up to?” And I said, “Well, I’m up here in Calgary shooting ‘Fargo.’” He said, “You guys are still doing that thing?”

How do you describe your character?

He’s really a member of the animal kingdom. Does he think he’s right or wrong? He’s an alligator. He has this thing to do. The only thing he has—and this is what got me about the character—is this bizarre sense of humor. He likes to f— with people. It’s his only social life or recreation. It’s like jet skiing or camping to Malvo to f— with someone.

The name: Lorne Malvo. Is it a coincidence that it sounds like Lee Malvo, the young man convicted in the D.C.-area sniper killings?

You know what, not until you said that. This entire time it didn’t occur to me once. The only thing I thought was about Lorne Greene on “Bonanza.” Lorne Malvo sounds like such a classic name. Like someone that Gary Cooper might have played in a Western, or a bass player in a rockabilly band. A little antiquated but kind of cool. It’s a name from 1962.

How did you play that mix between threatening and witty?

It depends on which character he’s talking to. When I [Malvo] am talking to Oliver Platt, I’m working and I don’t necessarily want to chitchat. I show him who I am. But with the cop, Gus, played by Colin Hanks, it’s in between. Is he nice? Is he serious? Malvo is a snake charmer. You look in his eyes and you do what he says because you know he means it. It doesn’t matter that I weigh 135 pounds. I can tell a guy who’s 6-4 and his henchmen, “I’m just stopping by to have a look at you.” A Jack Russell terrier will fight a German Shepherd. It doesn’t give a sh—. Malvo has an unlimited amount of confidence and an animal instinct for smelling fear and weakness. He doesn’t even think that he might lose. It’s like a guy who walks on hot coals. If he thinks about the heat, it’s gonna burn.

And he’s a keen observer.

He’s vastly interested in people. But he also has an agenda at the end of the day. He thinks, how can I use this person to fit into my plan?

The Midwestern accents are very exaggerated, so Malvo stands out without one.

Noah didn’t want an accent. He just wanted mine, because you’re not supposed to know where he’s from. We didn’t talk about it, but I assume that Malvo has done this all over the place. He probably ran a scheme in San Diego. Then went over to Alabama, Mississippi, Florida for sure. Probably went to Wisconsin and ultimately over to Duluth.

Did you see any similarities to Anton Chigurh, the killer played by Javier Bardem in the Coens’ “No Country For Old Men”?

It was mentioned to me about halfway through shooting, but it had never occurred to me. The only Coen brothers character I thought about was Ed Crane, the guy I played in “The Man Who Wasn’t There.” If Ed Crane, who was very silent and still, had this sick, dark brother, he might be like Malvo.

Having shot with the Coens, did anything seem familiar on the set of the show, because on the TV series they tried to mirror a Coen brothers’ look.

Not so much. But as a director, I’m aware of what they’re shooting: This is a close up with a wide angle lens and they’re shooting it from the corner. But Noah does remind me of Ethan a lot. I called him Ethan a couple times by mistake. There’s some physical similarities. A little scruffy growth on the chin and glasses. But the main thing is, when you ask Noah, “So what did you think about the scene?” He’ll say, “Yeah, it’s good.” For Noah, that’s huge. And if Joel or Ethan says, “Yeah, it’s good.” That’s like you or me saying, “That’s f—-ing stupendous.” Not real forthcoming with their emotions. You get to be a student of their body language.

Isn’t it strange that “Fargo” is synonymous with the Coen brothers, but it’s owned and controlled by someone else, in this case MGM? Of course that’s how the movie business works, but the gap between creative property and intellectual property is striking.

That’s funny, because someone asked me if I’d ever do a sequel to “Sling Blade.” Well, it’s a little sacred to me and I’m not sure, but maybe if I came up with a good idea for one, sure. Then afterward, I asked my manager if it would even be possible. Because I did “Sling Blade” on the stage as a one-man show. Then there was a short film and then the feature film. And it turns out that I don’t think I could do a sequel without a lot of lawyers and red tape. This is a character that nobody had anything to do with but me, but I really don’t own it. I won an Academy Award for best adapted screenplay—adapted from my own work. Which is weird, isn’t it?

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